Accident Analysis and Prevention 50 (2013) 861–870
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Accident Analysis and Prevention
journal homepage: www.elsevier.com/locate/aap
Impact of grade separator on pedestrian risk taking behavior
Mariya Khatoon a,b,∗ , Geetam Tiwari c,b,1 , Niladri Chatterjee a,2
a
Department of Mathematics, IIT Delhi, India
Transportation Research and Injury Prevention Program (TRIPP)/IIT Delhi, India
c
Department of Civil Engineering, IIT Delhi, India
b
a r t i c l e
i n f o
Article history:
Received 30 December 2011
Received in revised form 5 July 2012
Accepted 10 July 2012
Keywords:
Pedestrian behavior
Pedestrian risk
Grade separator
Gap acceptance
Logistic regression
a b s t r a c t
Pedestrians on Delhi roads are often exposed to high risks. This is because the basic needs of pedestrians are not recognized as a part of the urban transport infrastructure improvement projects in Delhi.
Rather, an ever increasing number of cars and motorized two-wheelers encourage the construction of
large numbers of flyovers/grade separators to facilitate signal free movement for motorized vehicles,
exposing pedestrians to greater risk. This paper describes the statistical analysis of pedestrian risk taking
behavior while crossing the road, before and after the construction of a grade separator at an intersection
of Delhi. A significant number of pedestrians are willing to take risks in both before and after situations.
The results indicate that absence of signals make pedestrians behave independently, leading to increased
variability in their risk taking behavior. Variability in the speeds of all categories of vehicles has increased
after the construction of grade separators. After the construction of the grade separator, the waiting time
of pedestrians at the starting point of crossing has increased and the correlation between waiting times
and gaps accepted by pedestrians show that after certain time of waiting, pedestrians become impatient
and accepts smaller gap size to cross the road. A Logistic regression model is fitted by assuming that
the probability of road crossing by pedestrians depends on the gap size (in s) between pedestrian and
conflicting vehicles, sex, age, type of pedestrians (single or in a group) and type of conflicting vehicles.
The results of Logistic regression explained that before the construction of the grade separator the probability of road crossing by the pedestrian depends on only the gap size parameter; however after the
construction of the grade separator, other parameters become significant in determining pedestrian risk
taking behavior.
© 2012 Elsevier Ltd. All rights reserved.
1. Introduction
As per the accident data, among all road users in Delhi, the ones
who are most exposed to risk are the pedestrians. Pedestrian deaths
in Delhi are about 4 times the national average. Fig. 1 shows the
share of pedestrian fatalities in Delhi from 2001 to 2009 (Delhi
Police, 2009); it indicates that pedestrians have the largest share
in total fatalities and the share remains the same over the years,
which is about 50% of the total fatalities.
Pedestrians are the most vulnerable and the ongoing infrastructure improvement projects in Delhi are making them even
more vulnerable (Gupta et al., 2010). It is therefore important to
∗ Corresponding author at: MS-804, Indian Institute of Technology (IIT) Delhi,
Hauz Khas, New Delhi 110016, India. Tel.: +91 11 2659 6092; fax: +91 11 2685 8703.
E-mail addresses: [email protected] (M. Khatoon), [email protected]
(G. Tiwari), [email protected] (N. Chatterjee).
1
Address: MS-815, Indian Institute of Technology (IIT) Delhi, Hauz Khas, New
Delhi 110016, India. Tel.: +91 11 2659 1047; fax: +91 11 2685 8703.
2
Address: MZ-167, Indian Institute of Technology (IIT) Delhi, Hauz Khas, New
Delhi 110016, India. Tel.: +91 11 2659 1490; fax: +91 11 2658 1005.
0001-4575/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.aap.2012.07.011
study pedestrian behavior in order that the risks faced by them
can be minimized while the transportation facilities are improved
for motorized traffic. Pedestrians are mainly exposed to risk when
crossing a road in urban areas as non-crossing accidents generally represent a small proportion of pedestrian accidents (Lassarre
et al., 2007; Duncan et al., 2002). A common phenomenon in Delhi
is that a pedestrian has to fight for space on the road, because of a
lack of safe and convenient pedestrian paths. In Delhi, a significant
investment has been made for the construction of flyovers/grade
separators to increase the speed of motorized vehicles, to reduce
their delay, and to make arterial roads in Delhi signal free. As
new grade separators are constructed the signalized crossings are
converted into signal free crossings, causing more problems for
pedestrians. Although a pedestrian often has the option of crossing
the road using the subway/foot over bridge most often they do not
use it. Rather, they prefer to cross the roads on the surface. Rasanen
et al. (2007) and Tanaboriboon and Jing (1994) confirmed this by
comparing signalized intersection pedestrian crossings to overpass
and underpass counterparts and found that pedestrians preferred
signalized at grade crossings to overpass or underpass crossings.
The objective of this study is to examine whether construction of
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M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
important explanatory variables included a number of vehicles in
the platoon, vehicle speed, pedestrian distance from kerb, number of pedestrians simultaneously crossing and city size, whereas
road width, median refuge, yield rules and most of the pedestrian
variables were not found to be significant.
52
50
48
46
44
42
2001
2002
2003
2004
2005
2006
2007
2008
2009
Pedestrians' Fatalities (%)
Fig. 1. Share of pedestrian fatalities in Delhi.
grade separators in place of signalized intersections has any significant effect on the risk taking behavior exhibited by different type of
pedestrians. It should be noted that after the construction of grade
separators, traffic signals are removed. As a consequence, there is
no safe signal, rendering all crossings unsafe. Thus pedestrians who
cross the road on the surface always face a risk.
1.1. Literature review
A number of studies have been conducted on the behavior and
movement of pedestrians at junctions and/or at other crossing locations. These studies include the impact of the road environment,
traffic environment and road safety treatments by means of before
and after studies on pedestrian’s behavior and safety.
1.1.1. Road and traffic environment
Li and Fernie (2010) studied the pedestrian behavior under different road surface conditions at a busy two-stage crossing. The
results show that a significant number of pedestrians fail to comply
with the delay involved in a two-stage crossing, leading to unsafe
crossing behavior. Jacobs et al. (1968) also found that when there
is a median refuge, non-compliance rates increase.
King et al. (2009) found that illegal crossing behavior is associated with an increased crash risk. Crossing against the lights
and crossing away from the lights both exhibited a crash risk per
crossing event approximately 8 times that of the legal crossing at
signalized intersections.
Rasanen et al. (2007) designed a study to find out factors that
influence use/non-use of pedestrian bridges. This study showed
that the factors influencing pedestrian perceptions of bridge use
are time saving, safety and familiarity of the area. It also suggests
that generally bridge use or non-use is a habit and not coincidental
behavior.
Leden (2002) calculated the risks for pedestrians as the expected
number of reported pedestrian accidents per pedestrian and found
that the risk decreased with increasing pedestrian flows and
increased with increasing vehicle flows.
Sisiopiku and Akin (2003) findings from an observational study
of pedestrian behavior at various urban crosswalks and a pedestrian user survey reported that unsignalized midblock crosswalks
were the treatment of preference to pedestrians and also showed
high crossing compliance rate of pedestrians. Crosswalk location,
relative to the origin and destination of the pedestrian, was the
most influential decision factor for pedestrians deciding to cross at
a designated location.
Himanen and Kulmala (1988) used multinomial Logit model
to examine pedestrian and driver reaction to “encounters” occurring at pedestrian crossings. The probabilities of a driver braking
or weaving, and of a pedestrian continuing to cross in response
to an encounter are identified for a variety of pedestrian, environmental, and traffic conditions. The results indicate that the most
1.1.2. Before and after studies
Keegan and O’Mahony (2003) evaluated the impact of the pedestrian waiting countdown timers and they found that these units
induced a reduction in the number of individuals who crossed during the red-man (do not walk) signal. Carsten et al. (1998) observed
the effect in pedestrian behavior and their safety, before and after
construction of innovative pedestrian signalized crossing and they
found that there were general gains in safety and comfort for pedestrians, and these improvements were obtained without major side
effects on vehicle travel. Hakkert et al. (2002) observed the impact
of a new type of uncontrolled pedestrian crossing which included
a system for detecting pedestrians near the crosswalk zone and for
warning drivers of pedestrian presence. Their findings suggest that
after the installation of the device there was a decrease of about
2–5 kmph in average vehicle speeds, an increase in the rate of giving
way to pedestrians and a significant reduction in vehicle pedestrian
conflicts in the crosswalk zone.
However, earlier studies have not attempted to quantify the risk
faced by pedestrians after providing free flow facilities to motorized vehicles. In this study we analyzed the risk taking behavior of
pedestrians when a signalized intersection is converted into a signal free intersection (grade separated). This study also examines
the combined impact of influencing variables to provide a better
estimate of pedestrian risk taking behavior.
2. Methodology
The aim of the study is to analyze the risk taking behavior of
pedestrians before and after the construction of a grade separator.
Data have been collected at an intersection when it was a four-way
signalized intersection in 1998 and was changed to a signal free
intersection by constructing a grade separator in 1999. Pedestrians had an option of crossing the road at the signalized crossing
safely or unsafely at grade when the intersection had a signalized
operation. After the construction of the grade separator at grade
crossing is always unsafe; safe crossing requires using a pedestrian underpass about 50 m from the intersection. We compared
pedestrians crossing the road unsafely at grade before and after
the construction of the grade separator. As a first step, pedestrian
risk has been defined. Afterwards, frequencies are compared for gap
size accepted and rejected by pedestrians, acceptance and rejection
of gaps with respect to different types of conflicting vehicles and
speeds of conflicting vehicles for both before and after construction
of the grade separator. Frequencies are also compared for the waiting time of pedestrians before and after construction of the grade
separator.
In order to see the impact of pedestrians’ waiting time on their
gap acceptance behavior, the correlation co-efficient is calculated
for both below and above average waiting time and accepted gaps.
A model is fitted to determine the probability that a pedestrian will
accept a gap size and start crossing the road. Here in this case the
outcome has two categories i.e. the pedestrian will cross the road
or not cross the road, hence “Binary Logistic regression model” is
used for the analysis. Gap size is defined as the difference between
the time when each pedestrian arrives at the crossing and each
conflicting vehicle enters at the crosswalk. The length of each gap
is calculated from the differences between the arrival times of two
consecutive vehicles, as indicated in Fig. 2. This available gap is
the gap presented to the pedestrian. If the pedestrian accepts the
M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
863
After a critical accepted gap size, i.e. a gap size after which
almost every gap is accepted by the pedestrian, the risk faced by
the pedestrian approaches zero.
The gap sizes accepted by pedestrians are not absolute. It
depends on the demographic parameters of the pedestrian, the
geometry of the road section, the intersection design and the traffic
characteristics. Many researchers have used gap size to model the
pedestrian crossing behavior as regards the time and/or location of
road crossings (Yang et al., 2006; Das et al., 2005; Oxley et al., 2005;
Simpson et al., 2003).
4. Pedestrian risk taking behavior
Fig. 2. Definition of gap size.
available gap (i.e., crosses the road within that gap), then it is an
accepted gap; otherwise it is a rejected gap.
Further, the “Binary Logistic regression model” is fitted considering that the probability of crossing the road depends also on other
parameters, such as sex, age, type of pedestrian (single or in a group)
and conflicting vehicle type.
3. Pedestrian risk
The risk faced by pedestrians while crossing the road has been
defined in different ways. In common life, risk is used as a very
broad concept including both the probabilities of an unwanted
event as well as the consequences of this event (Ekman, 1996).
The risk faced by pedestrians depends upon road crossing conditions that include presence and location of zebra crossings (Keall,
1995), signal cycle time for pedestrians (Tiwari et al., 2007), speed
of the conflicting vehicles (Pasanen, 1991), type of conflicting vehicle, intersection geometry (Lee and Abdel-Aty, 2005), waiting times
at different points of the intersection (Tiwari et al., 2007; Carsten
et al., 1998) and planning and designing of subways/foot over
bridges (Rasanen et al., 2007; Tanaboriboon and Jing, 1994). Previous research shows that the risk taking behavior of pedestrian
also depends on the pedestrian characteristics like sex and age
of pedestrian (Moyano Diaz, 2002; Rosenbloom and Wolf, 2002;
Hamed, 2001; Yagil, 2000; Oxley et al., 1997), whether they are
alone or in a group (Rosenbloom, 2009), nationality and educational
background (Al-Madani and Al-Janahi, 2006).
Historically, pedestrian safety monitoring has typically been
carried out using accident data, though given the rarity of such
events it is difficult to quickly detect change in pedestrian accident
risk at a particular site.
Elzein (2003) investigated a vision-based pedestrian detection
algorithm to calculate a time-to-collision parameter and stated that
pedestrians that have a relatively small time-to-collision are most
in danger of collision with the vehicle. Malkhamah et al. (2005)
stated that the most widely used non-accident based safety indicator is traffic conflicts; accident risk is only reliably correlated with
serious conflicts.
In view of the above, in the present work the risk is defined as
a function of “accepted gap size” (T) which is the measure of timeto-collision. When the accepted gap size increases, risk decreases.
The probability of risk would be 1 as the gap asymptotically goes
toward zero i.e. the situation of serious conflicts. Hence
Risk ∝
1
T
(1)
Risk taking behavior can be defined objectively (for example,
epidemiological data may show certain behaviors to be more likely
to result in injury than others) or subjectively (i.e. an individual’s
own perception of whether, or to what extent, a behavior is risky)
(Trimpop, 1994). The risk taking behavior of a pedestrian varies
with different type of road and traffic environments, their demographic, socio-economic profile and personal and social values (for
example, a pedestrian may become more conscious of take risk after
experiencing or witnessing a crash).
In this work, we studied the subjective probabilities in risk
taking behavior of pedestrians. The behavior studied was that of
pedestrians crossing a road against the moving traffic. It is assumed
that each pedestrian intended to cross the road safely but their perceptions about the chances of safely crossing a road is assumed to
be related to their characteristics, the gap size of oncoming vehicles,
etc.
4.1. Pedestrian risk taking behavior for two scenarios, before and
after the construction of the grade separator
The traffic signals that a pedestrian faces initially (before the
construction of the grade separator) can be categorized as “safe” or
“unsafe” according to whether a pedestrian crosses the road with
no interference from vehicles, or not. When a pedestrian crosses
the road at a safe signal (red signal for vehicles), the risk faced by
him/her is equal to 0. But when a pedestrian crosses the road at an
unsafe signal (green signal for vehicles), there is always some risk
associated with the crossing. In the before situation we analyzed the
pedestrians who crossed the intersection in an unsafe conditions.
After the construction of the grade separator, the traffic signal
was removed. As a consequence, there were no safe signals, rendering all at grade crossings unsafe. A pedestrian underpass has been
built about 50 m from the original intersection. In the after situation we analyzed the pedestrians who crossed the road at grade,
not using the underpass. In the absence of signals any pedestrian
crossing the road at grade is subjected to some risk because of the
continuous flow of incoming vehicles.
Since these numbers are also significant, an analysis of the
behavior of risk taking pedestrians is important from the pedestrian safety perspective. Hence the reported results of this study
apply to risk takers only, and not all pedestrians.
5. Data collection
To analyze the risk taking behavior of pedestrians and to find out
the change in it after the construction of the grade separator, data
have been collected by installing cameras near the AIIMS junction
on the Aurobindo Marg, a busy intersection in South Delhi where
a multi-directional grade separator was built in the year 1999. In
both the situations, we analyzed only those pedestrians who were
crossing the road at grade unsafely. The procedure of data collection
in detail is explained below.
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M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
N
INA
4
4
3
1
Main Gate
Moti Bagh
3
2
2
NOT DRAWN TO SCALE
3
Camera
SAFDERJUNG
HOSPITAL
1
1
2
AIIMS
Green Park
Fig. 3. Schematic intersection drawing before the construction of grade separator.
5.1. Configuration and operation of the intersection
The schematic view of the intersection before the construction of the grade separator is shown in Fig. 3. Fig. 4 describes
the schematic view of the intersection after the construction of
the grade separator showing the location of subway and grade
separator. This figure shows a superimposition of the intersection
geometry (drawn in black) after the construction of the grade separator on the intersection geometry (drawn in gray) before the
construction of the grade separator. Arrows show the directions
in which vehicles are permitted to travel. In Fig. 3 the arms of the
intersection are denoted clockwise as arms 1 through 4, and in Fig. 4
also the arms are denoted clockwise as arms 1 through 5.
Before the construction of the grade separator the placement
of the camera was such that it viewed the zebra crossing at arm 2
between points 1 and 3 as shown in Fig. 3. The distance between
points 1 and 2 was measured as 14.5 m and the distance between
the points 2 and 3 was measured as 13.4 m.
After the construction of the grade separator, one camera was
placed near the AIIMS main gate and the other was placed near the
Safdarjung hospital such that it could view the pedestrians crossing
between points 1 and 3 as shown in Fig. 4. The distance between 1
and 2 was measured as 22.25 m and the distance between 2 and 3
was measured as 19.8 m.
5.2. Videotaping, coding and interpreting the data
Data have been collected by video recording at the major pedestrian crossing of the AIIMS intersection. The crossing behavior of
pedestrians was noted by reviewing the video tapes. A high quality
digital camera equipped with a frame by frame timer (30 frames in
a second) was used to collect vehicle and pedestrian information
at each instant. The video tapes data were coded at the laboratory of the Transportation Research and Injury Prevention Program
(TRIPP), at the Indian Institute of Technology, Delhi. Each pedestrian
was viewed in slow motion by progressing the tape one frame (30
frames/s) at a time. The frames were displayed on a 29 in. screen
and data coding has been done. The tapes were viewed many times
to code all of the relevant information for pedestrians and vehicles.
Two sets of variables were coded for each pedestrian.
The first set describes the pedestrian’s attributes and movements. The coded attributes include sex, age group, and type of
pedestrian. The movement information includes the time of arrival
at the intersection, the time of crossing start, the time of arrival
and departure from the median, and the time at which crossing is
completed. The second set describes the vehicle’s attributes and
movements that include type and speed of conflicting vehicle and
the gap between two consecutive conflicting vehicles.
In the before situation, the median was present on the crossing
and in the after situation, a railing is present. In both the situations
pedestrians were doing staged crossings: first stage (from the edge
of the road to the median) and the second stage (from the median
to the other edge of the road). In this study we have analyzed the
risk taking behavior of pedestrians in the first stage of the crossing
only.
6. Analysis and discussion
6.1. Sample size
Before the construction of the grade separator the intersection
was signalized. Hence, pedestrians had the option to cross the road
safely (at the red phase for vehicles), although some pedestrians
were still committing an unsafe crossing (at the green phase of
vehicles), partially or fully. Before the construction of the grade separator situation we considered only those pedestrians in the sample
who committed an unsafe crossing. Therefore, in the data of 3953
gaps faced by 280 pedestrians, the analyzed sample contained only
457 gaps faced by 47 different pedestrians of which 410 gaps were
rejected and 47 gaps were accepted by the pedestrians. After the
construction of the grade separator, a total 108 pedestrians were
analyzed, all of them committing unsafe crossings because of an
absence of traffic signals. There were some pedestrians who used
the underpass. These were not included in the analysis. For the after
construction of the grade separator situation, the sample size was
700 gaps, faced by 108 different pedestrians, in which 592 gaps
were rejected and 108 gaps were accepted.
6.2. Pedestrian characteristics
Recording the sex of pedestrians was straightforward, and the
age was characterized into four broad age groups: child, young
adult, middle age and old from their appearance manually by the
data analysts. It was observed that males are involved in more road
crossings than females. Before the construction of the grade separator 80% of the pedestrians crossing the road were male and
20% were female while the corresponding figures are 71% and
29%, respectively for the period after the construction of the grade
M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
865
Fig. 4. Schematic intersection drawing after the construction of grade separator.
separator. Combining both we find that those who are involved
in road crossings comprise about 70–80% males and the rest are
females. Further we noticed that those who were involved in road
crossing primarily consist of young adults and middle aged people (approximately 90%). The number of children and old people
was very small in the data set. Hence, for further analysis these
categories were excluded from the data set because of insufficient
sample size. Again, we categorized the type of pedestrian in four
categories as single normal, handicapped, person in a group and
person with heavy baggage. But, because of insufficient sample size
(less than 5%) for further analysis, handicapped and persons with
heavy baggage were excluded categories from the data set.
6.3. Gap analysis
Mean rejected gap and mean accepted gap were observed from
the recorded data. Table 1 summarizes the findings. Levene’s test
tests the hypothesis that variance in groups are equal. Our results
show that for rejected gaps Levene’s test is significant i.e. variance in the rejected gaps before and after the construction of the
grade separator is not equal and for accepted gaps Levene’s test
is insignificant i.e. variance in the accepted gaps before and after
the construction of the grade separator is equal. Hence, for rejected
gap analysis t-value is observed by assuming that the variances of
two dataset are not equal whereas for accepted gap analysis t-value
is observed by assuming that the variance of the two datasets are
equal. One-tailed probability is used for rejected and accepted gaps
analysis because for both the cases mean of rejected and accepted
gaps are larger than after the construction of the grade separator.
Results indicate that in both the cases t-test is significant (at 99%
CI). It shows that mean rejected gap and mean accepted gap have
increased after the construction of the grade separator; i.e. after
the construction of the grade separator, pedestrians wait for bigger
gap size and because of uninterrupted flow of motorized vehicles
they do not easily find a sufficient gap size to cross. The variability
in both the rejected and the accepted gap has increased as well.
The increase of variability in people’s gap accepting behavior can
be ascribed to the non-existence of signals at the intersection. Signals make pedestrians wait and move according to the signal cycles.
However, the absence of signals make pedestrians behave independently, leading to increased variability in their risk taking behavior.
6.4. Analysis of gap vs. type of vehicle
Different types of conflicting vehicles have different impacts on
pedestrians’ road crossing behavior. Five categories of vehicles on
the road were taken into account for the analysis: heavy vehicle,
LCV (light commercial vehicle), car, motorized two-wheeler and
motorized three-wheeler. Before the grade separator construction,
a sample of size 457 different vehicles faced by the pedestrians was
considered, of which 47 vehicles were accepted. Among 237 cars
faced by pedestrians, 18 cars were accepted i.e. 7.59% cars. After
the construction of the grade separator the sample size taken for
the analysis was 700 different conflicting vehicles, of which 108
vehicles were accepted by pedestrians. Out of 317 cars faced by
pedestrians 40 were accepted i.e. 12.62%. Table 2 summarizes the
findings for all the vehicle types.
Table 2 shows that pedestrians’ acceptance of gaps has not been
very much affected by the vehicle type but pedestrian accepts
motorized two-wheeler more frequently in both the cases. It
appears from the analysis that the proportion of acceptance of vehicles has increased after the grade separator construction, except for
the LCVs. This may be an exception because there are very few LCVs
present in the traffic stream. For further analysis we excluded LCVs
from the dataset. The increase in the proportion of acceptance of
vehicles can be ascribed to the fact that before the grade separator
M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
(−3.588) (sig 0.00)
Table 2
Gap acceptance with respect to conflicting vehicles.
HV
LCV
Before grade separator
Acceptance (%)
7.69
83.33
After grade separator
18.46
Acceptance (%)
45.45
CAR
M2W
M3W
7.59
13.67
8.45
12.62
20.90
12.5
construction pedestrians had an option to wait for the safe signal.
After the construction of the grade separator there was no safe time
for pedestrians to cross the road at grade, therefore the proportion
of the acceptance of conflicting vehicles have increased.
F = 2.310 (sig
0.0655)
Levene’s test for
equality of
variances
t-value (equal
variances assumed)
866
Mean speed of conflicting vehicles and its standard deviation
have been calculated for before and after the construction of the
grade separator.
Table 3 shows that after the construction of the grade separator heavy vehicles, light commercial vehicles and motorized
two-wheelers are traveling at higher speeds as compared to before
the construction. Speed difference in cars is not significant while
the speed of motorized three-wheeler has decreased. Levene’s test
shows that the variability in the speeds of all categories of vehicles
has increased after the construction of the grade separator (at 95%
CI). As a consequence, risk to pedestrians increased after the construction of the grade separator as the variability in the speed of
the conflicting vehicles made the pedestrians more apprehensive
about crossing the road.
6.6. Pedestrians’ waiting time analysis
n is the number of observations.
Mean waiting time of the pedestrian has been observed at the
starting point of crossing and median of the road for before and
after construction of the grade separator.
Table 4 shows that after the construction of the grade separator,
mean waiting time of pedestrians has increased at the origin and
decreased at the median of the road i.e. pedestrians wait more at
the starting point of crossing. Before the construction of the grade
separator, people waited more at the median of road. It is also
observed that after the constructions of the grade separator pedestrians also wait moderately at other points of the road, looking for
an opportunity to cross the road.
a
2.6
4.05
5.48 (na = 47)
8.05 (na = 108)
(−7.727) (sig 0.00)
0.82
1.91
Before grade separator
After grade separator
0.64 (na = 410)
1.39 (na = 592)
F = 134.336 (sig
0.00)
Standard deviation
of accepted gap
Mean accepted gap
(in s)
t-value (equal
variances not
assumed)
Levene’s test for
equality of
variances
Standard deviation
of rejected gap
Mean rejected gap (in s)
Rejected gap analysis
Table 1
Rejected and accepted gap analysis.
Accepted gap analysis
6.5. Vehicles’ speed analysis
6.6.1. Correlation between waiting time and gaps accepted by
pedestrians
The correlation between waiting time and gap size accepted by
pedestrian before the construction of the grade separator was not
significant. This can be ascribed to the fact that before the grade
separator construction, pedestrian find safe at grade crossing after
certain time of waiting and only those pedestrian cross the road
unsafely who did not want to wait. After construction of the grade
separator, the correlation between the waiting time of the pedestrians at the origin and the gap size accepted by them was observed.
A sample of 62 non-zero waiting time faced by the pedestrians was
taken into account. Some of the pedestrians did not wait while
they crossed the road, without waiting even for a second at the
point they started crossing. But only those pedestrians were considered in the analysis, who had some waiting time at the origin.
In that sample, minimum, maximum and average waiting time
were 1 s, 127 s and 14.5 s, respectively. Further, the correlation was
found between the waiting time and the accepted gap in two separate parts. In the first part, the correlation between the waiting
times, which was below the average waiting time (14.5 s) and the
accepted gap was observed. In this case the value of correlation
M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
867
Table 3
Mean speeds of conflicting vehicles.
Conflicting vehicle
CAR
HV
LCV
M2W
M3W
Before construction of grade separator
After construction of grade separator
Mean speed
(km/h)
Standard
deviation
Mean speed
(km/h)
Standard
deviation
27.58 (n = 237)
28.76 (n = 26)
29.11 (n = 6)
27.35 (n = 117)
25.12 (n = 71)
7.65
7.57
1.21
7.63
9.01
26.55 (n = 317)
34.56 (n = 65)
55.66 (n = 11)
31.30 (n = 179)
22.04 (n = 128)
13.94
9.93
5.88
12.6
9.52
co-efficient was +0.1474 (positive and significant at 95% CI). It
shows that till the average waiting time, as the waiting time
increases the accepted gap size also increases i.e. people wait for a
larger gap size to cross. In the second part, the correlation between
the waiting times, which were above the average waiting time and
the accepted gaps, were obtained. In the second case, the value of
correlation co-efficient was obtained −0.0999 (negative and significant at 95% CI). It shows that when the waiting time was bigger
than the average waiting time, as the waiting time increases the
accepted gap size decreases.
The correlation analysis shows that people wait for bigger gaps
up to a certain time but after that they become impatient and accept
smaller gaps. This confirms the findings of our earlier study (Tiwari
et al., 2007) that higher pedestrian delays at the intersection result
in a higher number of unsafe crossings.
6.7. A probabilistic model for pedestrian’s risk taking behavior
A model is fitted to determine the probability that a pedestrian
will start crossing the road. In this model Xi ’s are independent variables and the dependent variable Y is a binary variable taking values
1 or 0. The value of Y = 1 shows that the pedestrian has accepted the
gap i.e. s/he has started crossing; whereas Y = 0 shows that pedestrian has rejected the gap, i.e. s/he still has not decided to cross.
Since the outcome in this case has two categories, the “Binary Logistic regression” was used. Let Pi be the probability of crossing the
road by a pedestrian, when the gap faced by him/her is Xi . Under
the Logistic regression Pi is related to Xi in a non-linear way, given
by the following equation:
Pi =
1
1 + exp(−ˇ0 − ˇ1 Xi )
t-Value
F = 187.733 (sig 0.00)
F = 3.751 (sig 0.05)
F = 13.613(sig 0.002)
F = 49.032 (sig 0.00)
F = 6.739 (sig 0.010)
1.024 (sig 0.269)
(−3.007) (sig 0.004)
(−14.423) (sig 0.00)
(−3.350) (sig 0.001)
2.268 (sig 0.025)
Table 4
Mean waiting time of pedestrian at origin and median of the road.
Before the grade separator
After the grade separator
Mean waiting time
at origin (s)
Mean waiting time
at median (s)
1.9
6.62
5.66
3.52
Table 5
Probability of road crossing at different gap sizes.
Gap size
2
4
6
8
11
12
Before the construction
of the grade separator
After the construction
of the grade separator
Probability of road
crossing (%)
Probability of road
crossing (%)
8.96
73.1
98.68
99.95
99.99
99.99
3.4
15.57
49.1
83.45
98.36
99.27
(2)
where ˇ0 and ˇ1 are the unknown parameters, need to be estimated.
The probability of crossing a road is dependent on other factors
as well. It is a function of other parameters, such as sex, age, type
of pedestrian and type of conflicting vehicle, etc. Hence, we tried to
jointly explain the impact of these variables on the probability of
road crossing by a pedestrian. Again, the Logit regression model is
fitted as follows:
1
Pi =
1 + exp(−Zi )
Levene’s test for equality of
variances
(3)
Zi = ˇ0 + ˇ1 × gap
size + ˇ2 × sex + ˇ3 × age + ˇ4 × ped
where
type + ˇ5 × veh type.Where the values of intercept (ˇ0 ) and
regression co-efficient (ˇi s), need to be estimated.
SPSS statistical software was used for the analysis. First to see
the impact of the gap size parameter on the road crossing of the
pedestrian and to analyze it in detail, we only consider the gap size
parameter in the model. For further analysis other parameters were
considered altogether. The findings of the analysis are discussed in
the following sections.
Fig. 5. Probability of crossing the road vs. gap before construction of grade separator.
6.7.1. Gap size is considered as an independent variable
From the samples for before and after the construction of the
grade separator, values of intercept (ˇ0 ) were −5.636 and −4.998,
respectively; values of Logistic regression co-efficient (ˇ1 ) were
1.659 and 0.827, respectively; and the model and gap size parameters were significant (sig value = 0) for both the cases. Table 5 shows
the probabilities of road crossing at different gap sizes.
From Table 5 the probability of crossing for the pedestrians with
the gap size, have been plotted in the graphs (Figs. 5 and 6). Both
the cases (before and after the grade separator construction) have
been analyzed separately.
From Figs. 5 and 6 it is clear that in both the before and after
situations, if the gap size is small the probability of crossing is very
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M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
the construction of the grade separator, pedestrian has no choice
of waiting for the “safe phase” for at grade crossing.
Fig. 6. Probability of crossing the road vs. gap after construction of grade separator.
low i.e. smaller gaps are not frequently accepted. As the gap size
increases the probability of crossing increases linearly. Before the
construction of the grade separator, after the gap of 6 s the probability of crossing for the pedestrians becomes almost 1. Thus, 6 s
is assumed to be the critical gap size i.e. a gap after which almost
every gap is accepted. This is for those pedestrians, who cross the
road unsafely at grade though the traffic signal was operative there.
Whereas, after the construction of the grade separator the critical gap size increases to 11 s because now safe crossing is possible
by using the underpass which is 50 m away and every pedestrian
crossing at grade has to cross the road with moving traffic.
Analysis shows that the probability of road crossing after the
construction of the grade separator is less, at the same gap size and
the critical gap faced by pedestrians is large. We ascribe this to two
reasons: first, variability in speed of traffic has increased after the
construction of the grade separator. As the variability in speed of
the conflicting vehicle is higher, it is a deterrent for the pedestrian,
to start crossing the road, even though the gap is of the same length.
Second, before the grade separator construction, pedestrians knew
that if they waited for a certain period, there will be a safe phase for
crossing the road. Hence they were inclined to wait in general. Only
those pedestrians crossed the road at a green phase, who wanted
to take the risk (young pedestrians, people in haste etc.). But after
6.7.2. Gap size, sex, age, pedestrian type and vehicle type are
considered as independent variables
The independent variables in the model are a mix of continuous and categorical. Logistic regression analysis has been done on
SPSS statistical software. Dummy coding method is used to code
independent categorical variables in Logistic regression. Dummy
coding is the comparisons in relation to the omitted reference category. The model considers that the probability of crossing a road
by pedestrians does not only depend on the gap size, but also on
different underlying parameters such as sex, age and type of pedestrian, and type of vehicles. Table 6 shows the omnibus tests of model
co-efficients and model summary.
The chi-square statistics in Table 6 indicate that both the models are statistically significant (sig value is 0.00). Thus, overall
the models are predicting the probability of road crossing significantly better than the model with only the constant included. The
log-likelihood statistic indicates that how much unexplained information is there after the models have been fitted. The value of
Nagelkerke R square is .791 and .709 for both the models before
and after construction of grade separator, indicating that both the
models are good enough to predict the outcome variables.
Table 7 describes the value of Exp(ˇ) and significant values of
predictor variables.
Table 7 shows the effect of different parameters in indulging in
risk taking crossing. The findings are as follows:
1. Gap size which represents the unit of time by which the vehicle
will reach the crossing line, is significant in both the cases (at
99% CI). Increased gap size increases the probability of crossing
the road by the pedestrian (value of odds ratio is greater than 1)
and this is true for both the before and after situations.
2. Sex and age are insignificant before the construction of the grade
separator; however these become significant (at 95% CI and 90%
CI, respectively) after the construction of the grade separator.
This can be attributed to the fact that before the construction of
the grade separator only those pedestrians crossed the road at
grade in the green phase for vehicles who could take a higher
risk while the others waited for the red phase for vehicles to
cross the road safely. But after the construction of the grade separator, no option was available for crossing the road safely at
grade. Therefore all pedestrians crossing at grade are exposed
Table 6
Omnibus tests and model summary.
Omnibus tests of model co-efficients
Before construction of grade separator
After construction of grade separator
Model summary
Chi-square
Degree of freedom
Sig value
−2 Log-likelihood
Nagelkerke R square
178.158
320.39
7
7
0
0
70.196
209.105
0.776
0.708
Table 7
Odds ratio and significant value of independent variables in Logistic regression.
Variables in the equation
Gap size
Male
Young adult
Single normal
Car
Heavy vehicles
Two-wheeler
Constant
*
Significant variable.
Before construction of grade separator
After construction of grade separator
Exp(ˇ)
Sig value
Exp(ˇ)
Sig value
5.961
1.667
0.612
0.467
0.236
0.009
0.965
0.014
0*
0.906
0.811
0.867
0.125
0.112
0.966
0.099
2.407
2.583
2.115
1.398
1.36
0.141
3.369
0.001
0*
0.033*
0.057*
0.384
0.561
0.053*
0.039*
0
M. Khatoon et al. / Accident Analysis and Prevention 50 (2013) 861–870
to risk hence sex and age becomes significant factors to determine the probability of the road crossing. After the construction
of the grade separator, males are associated with an increased
risk because the value of odds ratio is greater than 1 (at 95% CI),
odds of probability of crossing the road by the male is about 2.6
times higher than the female under the same situation. This confirmed the finding of Simpson et al. (2003), Rosenbloom (2009)
and Hamed (2001) that males take greater risks in road crossing than females. After the construction of the grade separator,
young adults are also associated with an increased risk because
the value of odd ratio is greater than 1 (at 90% CI), odds of probability of crossing the road by the young adult is 2.1 times higher
than the middle aged pedestrian. This shows that males and
young adults are more likely to take the risk. Rosenbloom et al.
(2004) confirmed that younger pedestrians are frequent violators. But, Oxley et al. (1997) found that on one-way divided roads,
older pedestrians’ crossing behavior was similar to that of the
younger pedestrians.
3. Pedestrian type (single or in a group) is insignificant in determining the probability of road crossing for both the cases i.e. before
and after the construction of the grade separator. Rosenbloom
(2009) examined the road behavior of individual pedestrians
compared to groups of pedestrians at the signalized intersection
and found that the tendency to cross on red was greater when
pedestrians cross the road in group. In the present study, we
found that probability of road crossing is similar when pedestrians cross alone and in a group for both before and after situations.
4. Before the construction of the grade separator all vehicle types
are insignificant but after the construction of the grade separator heavy vehicles and two-wheelers are significant (at 90% CI
and 95% CI, respectively) and the car is insignificant, if we take
motorized three-wheeler as a reference category. In the model
(after the construction of the grade separator) heavy vehicles are
associated with a decreased (value of odds ratio is less than 1)
and motorized two-wheelers are associated with an increased
(value of odds ratio is greater than 1) probability of road crossing comparative to three-wheelers. Values of odds ratio indicate
that the odds of the probability of crossing the road by a pedestrian is about 7.1 (1/0.141) times lower if the conflicting vehicle
is a heavy vehicle compared to a motorized three-wheeler and
the odds of the probability of crossing the road by a pedestrian
is about 3.4 times higher if the conflicting vehicle is a motorized
two-wheeler compared to motorized three-wheeler. The probability of crossing the road by a pedestrian is the same if the
conflicting vehicle is a car or a motorized three-wheeler.
869
tend to pedestrians accept a larger gap size. Before the construction of the grade separator the probability of road crossing by a
pedestrian depended on the gap size; however after the construction of the grade separator it also depends on sex, age and vehicle
types. Male and young adults have higher probability of road crossing as compared to female and older persons. Probability of road
crossing reduces when faced with a heavy vehicle (bus), whereas
it increases in the case of two-wheelers.
The results are basic inputs to the road crossing simulation,
needed to design well structured intersections. It highlights human
behavior and risk taking owing to road geometry and operations. Often traffic facilities are designed to ease the movement
of motorized traffic. This creates difficult and unsafe conditions
for pedestrians. Ideally traffic facilities must address the needs of
all road users equally. Traffic engineers and safety planners while
designing grade separators must ensure safe signalized crossings
in addition to subways or foot over bridges.
8. Limitation of the study
The focus of the work is to model the crossing behavior of risk
taking pedestrians who cross the road at grade in unsafe road
crossing conditions. Note that the risk taking behavior is defined
differently for the before and after situations. A significantly large
section of the pedestrians cross the road in the same place without taking the risk (e.g. crossing in green signal for pedestrians in
the before situation, and using the underpass in the after situation).
Such pedestrians are kept out of the scope of this study. The data
used for statistical analysis was from a video camera placed at a
place where the maximum number of pedestrians is found to be
crossing the road. However, there are still a number of pedestrians
who are engaged in risk taking crossing at other points. This data
was not captured by the video camera, and is therefore not within
the scope of this analysis. This study does not correlate the observed
risk to the actual crashes. To conduct such an analysis we need to
rely on police data over a much longer period of time. We intend to
do this analysis in the near future. The analysis is contextual. The
results obtained are meaningful and applicable for specific regions
with similar road users, road and traffic environment, administrative policies and practices.
Acknowledgement
This work was partially supported by grants from Volvo
Research and Educational Foundation (VREF).
7. Conclusions
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